## Luciano Rezzolla and Olindo Zanotti

Print publication date: 2013

Print ISBN-13: 9780198528906

Published to Oxford Scholarship Online: January 2014

DOI: 10.1093/acprof:oso/9780198528906.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see http://www.oxfordscholarship.com/page/privacy-policy). Subscriber: null; date: 26 February 2017

# (p.665) Appendix C Notable Tensors

Source:
Relativistic Hydrodynamics
Publisher:
Oxford University Press

We report below the most relevant tensors, in their component notation, that have been used in the derivation of the relativistic-hydrodynamic equations.

# C.1 Relativistic expressions

A detailed discussion of the properties of the tensors presented here can be found in Sections 3.1.1 and 3.7.4.

$Display mathematics$
(C.1)
$Display mathematics$
(C.2)
$Display mathematics$
(C.3)
$Display mathematics$
(C.4)
$Display mathematics$
(C.5)
$Display mathematics$
(C.6)
$Display mathematics$
(C.7)
$Display mathematics$
(C.8)
$Display mathematics$
(C.9)
$Display mathematics$
(C.10)
$Display mathematics$
(C.11)
$Display mathematics$
(C.12)
$Display mathematics$
(C.13)
$Display mathematics$
(C.14)
$Display mathematics$
(C.15)
$Display mathematics$
(C.16)
$Display mathematics$
(C.17)
$Display mathematics$
(C.18)
$Display mathematics$
(C.19)
$Display mathematics$
(C.20)
$Display mathematics$
(C.21)

(p.666) where η and ζ are the shear viscosity and the bulk viscosity, respectively.

# C.2 (p.667) Newtonian expressions

To aid comparison with classical textbooks, e.g., Landau and Lifshitz (1980), we report below the Newtonian expressions of the most relevant hydrodynamic tensors. A detailed discussion of the properties of the tensors presented here can be found in Section 2.2.6.

$Display mathematics$
(C.22)
$Display mathematics$
(C.23)
$Display mathematics$
(C.24)
$Display mathematics$
(C.25)
$Display mathematics$
(C.26)
$Display mathematics$
(C.27)
$Display mathematics$
(C.28)
$Display mathematics$
(C.29)
$Display mathematics$
(C.30)
$Display mathematics$
(C.31)
$Display mathematics$
(C.32)